Babylonian Tablet Plimpton 322: Ancient Sexagesimal Trigonometry Predates Greeks — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Plimpton 322 encodes exact sexagesimal reciprocal pairs that generate Pythagorean triples via a tangent half-angle parametrization of the unit circle, predating Greek trigonometry by a millennium. | MATH: The tablet lists 15 rows of (a, c) values with b² = c² − a². The underlying parametrization is equivalent to: x = (1 − t²)/(1 + t²), y = 2t/(1 + t²), where t = p/q in sexagesimal. The reciprocal pairs (p, q) satisfy p·q = 60^k (regular numbers), yielding exact rational points on the unit circle. Key ratios: c/a values range from 1.983 to 1.387 (sexagesimal: 1;59,00,15 to 1;23,13,46). The diagonal-to-short-side ratio (c/b) corresponds to tan(θ/2) = q/p, with θ the acute angle. | CONNECTION: The reciprocal pairs are regular sexagesimal numbers — their prime factors are only 2, 3, 5 — linking directly to base-60 arithmetic. The tangent half-angle substitution is the rational parametrization of the unit circle, whose integer solutions (Pythagorean triples) are lattice poi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222882969
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